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It appears that the relative maximum occurs between \(-1\) and \(0\). One can try a simple plot: plot(x -> 1/x, - 3, 3) Let's look at the function \(f(x) = 1/x\), which has an obvious vertical asymptote at \(0\). With julia you basically do the same thing, though panning and zooming is done by changing the domain of the \(x\) values used in plotting. What to do? If you were on a smartphone, you might be tempted to pan around to avoid the asymptotes, then pinch and zoom narrow the graph to the feature of interest. With only a finite number of pixels available, it is impossible to easily do both. However, if you have a vertical asymptote on the same graph, the \(y\) values might also be asked to show very large or small values. horizontal asymptotes (or even slant ones)įor example, if you want to find zeroes of a function, you really want to look at areas of the graph where the \(y\) values are close to \(0\).Some features of a graph that are identifiable by calculus concepts are: Keep in mind: while a graphic can highlight different features of a graph, it is often not possible to look at all of them on one graph. As well, the plot function does not handle cases where you get Inf for an answer (values that can come up when division by 0 is possible). The vertical asymptotes require care when plotting, as the naive style of plotting where a collection of points is connected by straight lines can render poor graphs when the scale of \(y\) values get too large. These can be vertical (which can happen when \(q(x)=0\)), horizontal (as \(x\) gets large or small), or even slant. One interesting thing about them is there can be asymptotes. A rational function is nothing more than a ratio of polynomial functions, say \(f(x) = p(x)/q(x)\).